why's r(t) the input and not t?
Because the right hand side of that equation denotes a function of t.
r(t) could be t but it can also be every other function that depends on t.
Basically, r(t) is the most general form to denote "a function of t"
That's not really mathematics- it's "Engineer speak".
From the point of view of an Engineer, a differential equation is a machine to which you supply an "input" and get an "output". The differential operator y"+ y'+ y is the machine. Whatever function you have on the right hand side is the "input" (which varies with t) and y(t) satisfying the equation is the "output".
(Edited- thanks, Marlon.)
The differential operator is not y''+y' but y''+y'+y
thank you very much!!!
Separate names with a comma.